152
4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
wave the initial development of the quasi-oscillation strongly influences the
non-linear evolution.
Conclusions. Wind waves appear to be a random hydrodynamic process.
To simplify wind wave investigation the quasi-stationary state interval (of the
order of 20 min) was usually used (Davidan et al., 1978). The main statistical
wave parameters were commonly considered as being approximately constant.
However, investigations performed during the last few decades revealed that
dispersion and the spectrum of the wave process change significantly within
this interval. It is important to note that these variations are larger than the
sample variability.
In the present book, numerical simulations of the energy balance equation
are carried out to estimate the influence of the wind wave parameter fluctuation on the non-linear spectrum evolution. The non-linear energy transfer
in the wave spectrum is calculated with the help of the original numerical
integrating method of highest accuracy. The results of numerical simulations
reveal that wind wave parameter fluctuation produces a significant increasing effect on the non-linear wave spectrum evolution. Its contribution at the
initial stage of wind wave development is the most significant. The effect of
quasi-oscillation becomes smaller for a developed wind sea.
The discontinuous character of the non-linear evolution of the spectrum
maximum frequency with oscillations (see Fig. 4.25) reveals that quasioscillations can be a starting mechanism of low-frequency spectrum evolution.
However, it does not operate within each quasi-oscillation period, but only at
a specific moment. It takes place when the non-linear spectrum evolution is
accumulated and changes the spectrum in such a way that it is sufficient to
make a "small push" to transfer the spectral maximum frequency to another
level.
The four-wave energy transfer is a non-linear mechanism depending on the
spectral density in powers of three, contrary to the wind wave energy input
or quasi-linear wave dissipation (Komen et al., 1994). Therefore, wind wave
models usually underestimate the contribution of the mechanism to the wave
spectral structure development. The non-linear energy transfer computed for
the averaged spectrum is much less than the same total value for the spectrum
with quasi-oscillations. The parameterization taking into account the effect
of quasi-oscillations in the spectral models of wind waves is proposed in the
present investigation.
4 Physical Mechanisms Forming the Wave Spectrum in Deep Water
wave the initial development of the quasi-oscillation strongly influences the
non-linear evolution.
Conclusions. Wind waves appear to be a random hydrodynamic process.
To simplify wind wave investigation the quasi-stationary state interval (of the
order of 20 min) was usually used (Davidan et al., 1978). The main statistical
wave parameters were commonly considered as being approximately constant.
However, investigations performed during the last few decades revealed that
dispersion and the spectrum of the wave process change significantly within
this interval. It is important to note that these variations are larger than the
sample variability.
In the present book, numerical simulations of the energy balance equation
are carried out to estimate the influence of the wind wave parameter fluctuation on the non-linear spectrum evolution. The non-linear energy transfer
in the wave spectrum is calculated with the help of the original numerical
integrating method of highest accuracy. The results of numerical simulations
reveal that wind wave parameter fluctuation produces a significant increasing effect on the non-linear wave spectrum evolution. Its contribution at the
initial stage of wind wave development is the most significant. The effect of
quasi-oscillation becomes smaller for a developed wind sea.
The discontinuous character of the non-linear evolution of the spectrum
maximum frequency with oscillations (see Fig. 4.25) reveals that quasioscillations can be a starting mechanism of low-frequency spectrum evolution.
However, it does not operate within each quasi-oscillation period, but only at
a specific moment. It takes place when the non-linear spectrum evolution is
accumulated and changes the spectrum in such a way that it is sufficient to
make a "small push" to transfer the spectral maximum frequency to another
level.
The four-wave energy transfer is a non-linear mechanism depending on the
spectral density in powers of three, contrary to the wind wave energy input
or quasi-linear wave dissipation (Komen et al., 1994). Therefore, wind wave
models usually underestimate the contribution of the mechanism to the wave
spectral structure development. The non-linear energy transfer computed for
the averaged spectrum is much less than the same total value for the spectrum
with quasi-oscillations. The parameterization taking into account the effect
of quasi-oscillations in the spectral models of wind waves is proposed in the
present investigation.